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PreprintCC BY 4.0arXiv

𝒡-stable and selfless inclusions for the infinite braid group

  • Tron Omland
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Abstract

Let B∞ be the braid group on infinitely many strands and P∞ its pure braid group. We show that C*r(P∞)βŠ† C*r(B∞) and all its intermediate inclusions are 𝒡-stable and completely selfless. This gives natural examples of simple nonnuclear 𝒡-stable C*-algebras. Further examples come from SL∞(β„€) and GL∞(β„€). We also show that C*r(π”½βˆž)βŠ† C*r(B∞) is completely selfless for the free group π”½βˆž of braids in which only the first strand moves. All results hold for twisted group C*-algebras. In contrast, 𝒡-stability fails for Bn with n finite and for groups that are not inner amenable.

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Cite

BibTeXRIS
BibTeX
@misc{omland2026𝒡stable,
  title = {{$\mathcalZ$-stable and selfless inclusions for the infinite braid group}},
  author = {Tron Omland},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.38596},
  eprint = {2609.38596},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.38596},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - 𝒡-stable and selfless inclusions for the infinite braid group
AU  - Tron Omland
PY  - 2026
DA  - 2026/10/26
PB  - arXiv
DO  - 10.48550/arxiv.2609.38596
UR  - https://arxiv.org/abs/2609.38596
AB  - Let B_∞ be the braid group on infinitely many strands and P_∞ its pure braid group. We show that C^*_r(P_∞)βŠ† C^*_r(B_∞) and all its intermediate inclusions are 𝒡-stable and completely selfless. This gives natural examples of simple nonnuclear 𝒡-stable C^*-algebras. Further examples come from SL_∞(β„€) and GL_∞(β„€). We also show that C^*_r(𝔽_∞)βŠ† C^*_r(B_∞) is completely selfless for the free group 𝔽_∞ of braids in which only the first strand moves. All results hold for twisted group C^*-algebras. In contrast, 𝒡-stability fails for B_n with n finite and for groups that are not inner amenable.
ER  -